Empirical descriptors, quantum-chemical

The primary supposition of any toxicological QSAR is that the potency of a compound is dependent upon its molecular structure, which is typically quantified by chemical properties (Schultz et al., 2002). Chemical descriptors include a variety of types, including atom, substituent, and molecular parameters. The most transparent of these are the molecular-based empirical and quantum chemical descriptors. Empirical descriptors are measured descriptors and include physicochemical properties such as hydrophobicity (Dearden, 1990). Quantum chemical properties are theoretical descriptors and include charge and energy values (Karelson et al., 1996). Physicochemical and quantum chemical descriptors are for the most part easily interpretable with regard to how that property may be related to toxicity. The classic example of this, the partitioning of a toxicant between aqueous and lipid phases, has been used as a measure of hydrophobicity for over a century (Livingstone, 2000). 

Semi-empirically AMl-obtained, but ad iiii/io-validated, quantum-chemical descriptors (HOMO, and... 

The aforementioned macroscopic physical constants of solvents have usually been determined experimentally. However, various attempts have been made to calculate bulk properties of Hquids from pure theory. By means of quantum chemical methods, it is possible to calculate some thermodynamic properties e.g. molar heat capacities and viscosities) of simple molecular Hquids without specific solvent/solvent interactions [207]. A quantitative structure-property relationship treatment of normal boiling points, using the so-called CODESS A technique i.e. comprehensive descriptors for structural and statistical analysis), leads to a four-parameter equation with physically significant molecular descriptors, allowing rather accurate predictions of the normal boiling points of structurally diverse organic liquids [208]. Based solely on the molecular structure of solvent molecules, a non-empirical solvent polarity index, called the first-order valence molecular connectivity index, has been proposed [137]. These purely calculated solvent polarity parameters correlate fairly well with some corresponding physical properties of the solvents [137]. 

Abstract In this chapter we give an overview on QSAR models for treating the mutagenicity of cyclic amines. An extensive discussion is focused on the topological. E-state, quantum chemical, and empirical descriptors (log ) that are often used in corresponding models. Two case studies are presented in more detail. The conclusion addresses the OECD principles for validation of models that are used for regulatory purposes. 

The class of the empirical descriptors is a fuzzy, not well-defined class. In principle, empirical descriptors are those not defined on the basis of a general theory such as, for example, quantum chemistry or graph theory. Rather they are defined by practical rules derived from chemical experience, e.g. considering specific or local structural factors present in the molecules, often sets of congeneric compounds. As a consequence, in most cases, empirical descriptors represent limited subsets of compounds and cannot be extended to classes of compounds different from those for which they were defined. Empirical descriptors have not to be confused with experimentally derived descriptors even if it is well known that several of them are empirically derived. 

As an alternative to ab initio methods, the semi-empirical quantum-chemical methods are fast and applicable for the calculation of molecular descriptors of long series of structurally complex and large molecules. Most of these methods have been developed within the mathematical framework of the molecular orbital theory (SCF MO), but use a number of simplifications and approximations in the computational procedure that reduce dramatically the computer time [6]. The most popular semi-empirical methods are Austin Model 1 (AMI) [7] and Parametric Model 3 (PM3) [8]. The results produced by different semi-empirical methods are generally not comparable, but they often do reproduce similar trends. For example, the electronic net charges calculated by the AMI, MNDO (modified neglect of diatomic overlap), and INDO (intermediate neglect of diatomic overlap) methods were found to be quite different in their absolute values, but were consistent in their trends. Intermediate between the ab initio and semi-empirical methods in terms of the demand in computational resources are algorithms based on density functional theory (DFT) [9]. 

The quantum-chemical descriptors have also shown their usefulness in the development of QSARs for antiviral activities. The antirhinoviral activity of 9-benzylpurines has been correlated with Huckel MO-generated electronic parameters and empirical substituent constants [99]. The respective QSAR equation included the LUMO energy and the total 7r-electron energy (EnT) of the compounds as quantum-chemical descriptors ... 

Other pharmacological activities have also been correlated with quantum-chemically derived descriptors. For instance, the quantitative structure-activity relationship developed for the antibacterial activity of a series of monocyclic (i-lactam antibiotics included the atomic charges, the bond orders, the dipole moment, and the first excitation energy of the compound [103]. The fungicidal activity of A3-l,2,4-thiadiazolines has been correlated with an index of frontier orbital electron density derived from semi-empirical PM3 molecular orbital calculations [104],... 

Quantum-chemical methods (Dewar and Thiel, 1977 Dewar et al, 1985 Stewart, 1989) may be applied to obtain a large variety of stereo-electronic descriptors such as ionization potential, polarizability, electron affinity, dipole moment, charge densities, HOMO- and LUMO-energies or atomic charges using semi-empirical or ab initio calculations (Table 1.4). 

The descriptors obtained generally refer to the ground state of the molecules under gas-phase conditions, which may not correspond to the solvatized compounds or their transition states involved in interactions in environmental phases. Additionally, the currently used quantum-chemical descriptors do not contain any entropy terms. The different semi-empirical calculation schemes, such... 

It is noteworthy that high quality QSARs cannot be developed if the critical factors related to bio activity are not present in the set of descriptors chosen. This is well illustrated with the activity of diastereoisomeric insect repellents. These molecules differ only in the spatial configuration of atoms. All topological, geometrical, and quantum chemical indices will have identical (redundant) values for the various diastereomers corresponding to the same empirical formula. Such situations call for novel approaches. As evident from our results on hierarchical overlay, the comparison of good quality structures generated by quantum chemical methods is needed in such cases. 

The mentioned study raises further questions Does QSAR benefit from quantum chemical descriptors and is there a place for such descriptors After all the computational effort to obtain quantum chemical descriptors is not negligible, particularly if many or large molecules are considered. Instead of using ab initio or density functional calculations, one might thus switch to semi-empirical molecular orbital theory. To clarify the feasibility... 

In principle, there are two strategies for molecular design. The first strategy is to start from the first principle, i.e., from quantum mechanics and statistical mechanics to predict the property of unknown materials. Up to now, however, it is still impossible to use this strategy to solve the most of complicated problems in materials exploration work. The second way is a semi-empirical one. It starts from the known data of some molecules and some molecular descriptors (including quantum chemical parameters) to find semi-empirical rules, and then use these empirical rules to predict the property of unknown molecules. The second way is already practicable for molecular design or new materials exploration. 

The molecular descriptors obtained by computation of molecular mechanics and quantum chemical methods are used to describe the molecular structures of A -(3-Oxo-3,4-dihydro-2//-benzo[l,4]oxazine-6-carbonyl) guanidines. The three-dimensional structures of the molecules are optimized with the software Hyperchem. Prior to the semi-empirical quantum chemical computation, all structures of the compounds are submitted to MM+ computation of molecular mechanics for energy optimization. The structural descriptors are obtained via the computation of semi-empirical method PM3. The computations are carried out at restricted Hartree-Fock level without configuration interaction. 

Fortunately, there are a number of theoretical, statistical and empirical reasons to believe that Lewis basicity (affinity) depends on a limited number of factors. From the quantum chemical point of view, the acid/base interaction energy can be partitioned into five terms (electrostatic, dispersion, polarization, charge transfer and exchange-repulsion). By a principal component analysis [184], 99% of the variance of an afflnity/basicity data matrix can be explained by three factors, the first two being by far the most important. A number of experimental affinity and basicity scales, and of spectroscopic scales of basicity, can be correlated by two parameters, using the EC or equations, or three quantum chemical descriptors of basicity [197]. However, these statistical and empirical approaches are limited to systems where steric effects and tt back-bonding are not important. 

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